Calculadora de Distribuição de Rayleigh

The Rayleigh Distribution Calculator is a statistical tool that computes the cumulative probability P(X ≤ x) for a random variable with a Rayleigh distribution. The Rayleigh distribution is commonly used to model the magnitude of two-dimensional vectors, such as the distance from a point to the origin in polar coordinates, or the amplitude of signals in wireless communication. The formula used is F(x) = 1 − exp(−x²/(2σ²)), where σ is the scale parameter of the distribution.

To use the calculator, you need to provide the value of x (the point up to which you want to accumulate probability) and the parameter σ (sigma). The result is the probability that the random variable is less than or equal to x. This tool is useful in fields such as engineering, physics, and reliability, where the Rayleigh distribution naturally arises. For example, it can be used to calculate the probability that a particle travels a certain distance in a random medium.

Important considerations: ensure that the data actually follows a Rayleigh distribution, which is positively skewed. The parameter σ must be positive. Additionally, the Rayleigh distribution is a special case of the Weibull distribution with shape parameter equal to 2. If your data does not fit this shape, other models may be more appropriate. Always verify model adequacy before using the results.